Sunflower seeds: $0.75 per pound
Pumpkin seeds: $0.50 per pound
How many pounds of sunflower seeds and pumpkin seeds are in this order?
Start by writing an expression to represent the cost of s pounds of sunflower seeds. Keep in mind that 1 pound of sunflower seeds costs $0.75
Cost of s
pounds of
sunflower seeds
+
Cost of p pounds of pumpkin seeds
=
Total Cost
+
?
=
?
Nice!
Now, add an expression to represent the cost of p pounds of pumpkin seeds. Keep in mind that 1 pound of pumpkin seeds costs $0.50.
Cost of
s
pounds of sunflower seeds
+
Cost
of
p
pounds of
pumpkin seeds
=
Total Cost
0.75s
+
=
?
Good work!
Finally, what do you need to set the expression equal to? Reread the problem to determine the total cost of the order.
Cost of sunflower seeds
+
Cost of pumpkin seeds
=
Total
Cost
0.75s
+
0.5p
=
Great job!
What equation could we write to represent that the number of pounds of sunflower seeds and the number of pounds of pumpkin seeds weighed a total of 20 pounds? Let s represent the number of pounds of sunflower seeds and p represent the number of pounds of pumpkin seeds.
Cost of sunflower seeds
+
Cost of pumpkin seeds
=
Total
Cost
0.75s
+
0.5p
=
13
Number of
pounds of sunflower seeds
+
Number of
pounds of pumpkin seeds
=
Total weight
of the order
+
=
Great job!
One way to solve this system is to substitute the value of one variable into the other equation. To do this, we can use either variable, p or s. So, we need to know either: p = some value, so that we can substitute that value for p, or, s = some value, so that we can substitute that value for s. Is either equation written as p equals some value or s equals some value yet?
0.75s+0.5p = 13
s+p = 20
Yes or No?
1 answer
No, neither equation is currently written in a form where one variable is isolated (i.e., expressed as "p = some value" or "s = some value"). We need to manipulate one of the equations to isolate one of the variables.
For example, we can take the second equation (s + p = 20) and solve for p:
\[ p = 20 - s \]
Now we can substitute this expression for p into the first equation (0.75s + 0.5p = 13). This will allow us to solve for s.
